(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 10.4' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     82804,       2951]
NotebookOptionsPosition[     68412,       2482]
NotebookOutlinePosition[     76047,       2701]
CellTagsIndexPosition[     75931,       2695]
WindowTitle->Integrate2
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[GridBox[{
   {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "See Also",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"See Also", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"DeltaFunction\"\>":>
       Documentation`HelpLookup[
       "paclet:FeynCalc/ref/DeltaFunction"], "\<\"Integrate3\"\>":>
       Documentation`HelpLookup[
       "paclet:FeynCalc/ref/Integrate3"], "\<\"Integrate4\"\>":>
       Documentation`HelpLookup[
       "paclet:FeynCalc/ref/Integrate4"], "\<\"Integrate5\"\>":>
       Documentation`HelpLookup[
       "paclet:FeynCalc/ref/Integrate5"], "\<\"SumS\"\>":>
       Documentation`HelpLookup["paclet:FeynCalc/ref/SumS"], "\<\"SumT\"\>":>
       Documentation`HelpLookup["paclet:FeynCalc/ref/SumT"]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"SeeAlso"]],
      LineSpacing->{1.4, 0}],
     "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\
\[ThickSpace]",
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "URL",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"URL", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"FeynCalc/ref/Integrate2\"\>":>
       None, "\<\"Copy Wolfram Documentation Center URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell["FeynCalc/ref/Integrate2"]}, Visible -> False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; Null], 
       Delimiter, "\<\"Copy web URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell[
              BoxData[
               MakeBoxes[
                Hyperlink[
                "http://reference.wolfram.com/language/FeynCalc/ref/\
Integrate2.html"], StandardForm]], "Input", TextClipboardType -> 
              "PlainText"]}, Visible -> False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; 
        Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{
         NotebookLocate[{
           URL[
            StringJoin[
             If[
              TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$170641], 
              "http://reference.wolfram.com/system-modeler/", 
              "http://reference.wolfram.com/language/"], 
             "FeynCalc/ref/Integrate2", ".html"]], None}]}]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"URLMenu"]],
      LineSpacing->{1.4, 0}]
    }], "AnchorBar"]}
  }]], "AnchorBarGrid",
 GridBoxOptions->{GridBoxItemSize->{"Columns" -> {
     Scaled[0.65], {
      Scaled[0.34]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
   "RowsIndexed" -> {}}},
 CellID->1],

Cell[TextData[{
 Cell["Integrate2", "ObjectName"],
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{8, 0}],
    CacheGraphics->False],
   Spacer[8]]]],
 Cell[BoxData[""], "ObjectNameTranslation"]
}], "ObjectNameGrid"],

Cell[CellGroupData[{

Cell[BoxData[GridBox[{
   {"", Cell[TextData[{
     Cell[BoxData["Integrate2"], "InlineFormula"],
     " \[LineSeparator]is like Integrate, but : Integrate2[a_Plus, b__] := \
Map[Integrate2[#, b]&, a] ( more linear algebra and partial fraction \
decomposition is done) Integrate2[f[x] DeltaFunction[x], x] \[Rule] f[0] \
Integrate2[f[x] DeltaFunction[x0-x], x] \[Rule] f[x0]. Integrate2[f[x] \
DeltaFunction[a + b x], x] \[Rule] Integrate[f[x] (1/Abs[b]) \
DeltaFunction[a/b + x], x], where abs[b] \[Rule] b, if b is a Symbol, and if \
b = -c, then abs[-c] \[Rule] c, i.e., the variable contained in b is supposed \
to be positive. ",
     Cell[BoxData[
      FormBox[
       RowBox[{" ", 
        SuperscriptBox["\[Pi]", "2"]}], TraditionalForm]]],
     " is replaced by 6 Zeta2. Integrate2[1/(1-y),{y,x,1}] is intepreted as \
distribution, i.e. as Integrate2[-1/(1-y)],{y, 0, x}] \[Rule] Log[1-y]. \
Integrate2[1/(1-x),{x,0,1}] \[Rule] 0."
    }]]}
  }]], "Usage",
 GridBoxOptions->{
 GridBoxBackground->{
  "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, 
   "RowsIndexed" -> {}}},
 CellID->982511436],

Cell[CellGroupData[{

Cell[TextData[Cell[BoxData[
 ButtonBox[Cell[TextData[{
   Cell[BoxData[
    InterpretationBox[
     StyleBox[
      GraphicsBox[{},
       BaselinePosition->Baseline,
       ImageSize->{6, 0}],
      CacheGraphics->False],
     Spacer[6]]]],
   "Details"
  }], "NotesFrameText"],
  Appearance->{Automatic, None},
  BaseStyle->None,
  ButtonFunction:>(FrontEndExecute[{
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], All, ButtonCell], 
     FrontEndToken["OpenCloseGroup"], 
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], After, CellContents]}]& ),
  Evaluator->None,
  Method->"Preemptive"]]]], "NotesSection",
 WholeCellGroupOpener->True,
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->106623255],

Cell["", "SectionHeaderSpacer"],

Cell["\<\
Since Integrate2 does do a reordering and partial fraction decomposition \
before calling the integral table of Integrate3 it will in general be slower \
compared to Integrate3 for sums of integrals. I.e., if the integrand has \
already an expanded form and if partial fraction decomposition is not \
necessary it is more effective to use Integrate3.\
\>", "Notes",
 CellID->1067943069]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "PrimaryExamplesSection",
 WholeCellGroupOpener->True,
 CellTags->"PrimaryExamplesSection",
 CellID->572860895],

Cell[CellGroupData[{

Cell[TextData[{
 "Basic Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "ExampleSection", "ExampleSection",
 WholeCellGroupOpener->True,
 CellID->439476420],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Integrate2", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"Log", "[", 
      RowBox[{"1", "+", "x"}], "]"}], 
     RowBox[{
      RowBox[{"Log", "[", "x", "]"}], "/", 
      RowBox[{"(", 
       RowBox[{"1", "-", "x"}], ")"}]}]}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], "//", 
  "Timing"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[1]:=",
 CellID->524907050],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{"0.028933`", ",", 
    RowBox[{
     TemplateBox[{"3"},
      "Zeta"], "-", 
     RowBox[{
      FractionBox["3", "2"], " ", 
      RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
      RowBox[{"log", "(", "2", ")"}]}]}]}], "}"}], TraditionalForm]], "Output",\

 ImageSize->{217, 34},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[TextData[{
 "Since Integrate2 uses table-look-up methods it is much faster than ",
 StyleBox["Mathematica",
  FontSlant->"Italic"],
 "'s Integrate."
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{"PolyLog", "[", 
    RowBox[{"2", ",", 
     RowBox[{"x", "^", "2"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[2]:=",
 CellID->546710902],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"\[Zeta]", "(", "2", ")"}], "-", "4", "+", 
   RowBox[{"4", " ", 
    RowBox[{"log", "(", "2", ")"}]}]}], TraditionalForm]], "Output",
 ImageSize->{128, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[2]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{"PolyLog", "[", 
    RowBox[{"3", ",", 
     RowBox[{"-", "x"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[3]:=",
 CellID->89878903],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[Zeta]", "(", "2", ")"}], "2"], "-", 
   FractionBox[
    RowBox[{"3", " ", 
     TemplateBox[{"3"},
      "Zeta"]}], "4"], "+", "1", "-", 
   RowBox[{"2", " ", 
    RowBox[{"log", "(", "2", ")"}]}]}], TraditionalForm]], "Output",
 ImageSize->{190, 34},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[3]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{"PolyLog", "[", 
    RowBox[{"3", ",", 
     RowBox[{"1", "/", 
      RowBox[{"(", 
       RowBox[{"1", "+", "x"}], ")"}]}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[4]:=",
 CellID->1742557754],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
    RowBox[{"(", 
     RowBox[{"-", 
      RowBox[{"log", "(", "2", ")"}]}], ")"}]}], "+", 
   FractionBox[
    RowBox[{"3", " ", 
     TemplateBox[{"3"},
      "Zeta"]}], "4"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox["log", "3"], "(", "2", ")"}], "3"], "-", 
   RowBox[{
    SuperscriptBox["log", "2"], "(", "2", ")"}], "+", 
   RowBox[{"2", " ", 
    RowBox[{"log", "(", "2", ")"}]}]}], TraditionalForm]], "Output",
 ImageSize->{362, 38},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[4]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"DeltaFunction", "[", 
     RowBox[{"1", "-", "x"}], "]"}], " ", 
    RowBox[{"f", "[", "x", "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[5]:=",
 CellID->1356840886],

Cell[BoxData[
 FormBox[
  RowBox[{"f", "(", "1", ")"}], TraditionalForm]], "Output",
 ImageSize->{34, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[5]="]
}, Open  ]],

Cell[TextData[{
 "Integrate2 does integration in a Hadamard sense, i.e., ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubsuperscriptBox["\[Integral]", "0", "1"], 
    RowBox[{
     RowBox[{"f", "(", "x", ")"}], 
     RowBox[{"\[DifferentialD]", "x"}]}], " "}], TraditionalForm]]],
 " means acutally expanding the result of ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    SubsuperscriptBox["\[Integral]", "\[Delta]", 
     RowBox[{"1", "-", "\[Delta]"}]], 
    RowBox[{
     RowBox[{"f", "(", "x", ")"}], 
     RowBox[{"\[DifferentialD]", "x"}]}], " "}], TraditionalForm]]],
 "up do ",
 Cell[BoxData[
  FormBox[
   RowBox[{"O", "(", "\[Delta]", ")"}], TraditionalForm]]],
 " and neglecting all ",
 Cell[BoxData[
  FormBox["\[Delta]", TraditionalForm]]],
 "-dependent terms. E.g. ",
 Cell[BoxData[
  FormBox[
   RowBox[{
    RowBox[{
     SubsuperscriptBox["\[Integral]", "\[Delta]", 
      RowBox[{"1", "-", "\[Delta]"}]], 
     RowBox[{
      RowBox[{"1", "/", 
       RowBox[{"(", 
        RowBox[{"1", "-", "x"}], ")"}]}], 
      RowBox[{"\[DifferentialD]", "x"}]}]}], " ", "=", " ", 
    RowBox[{
     RowBox[{
      RowBox[{
       RowBox[{"-", "log"}], 
       RowBox[{"(", 
        RowBox[{"1", "-", "x"}], ")"}]}], 
      SubsuperscriptBox["\[VerticalSeparator]", "\[Delta]", 
       RowBox[{"1", "-", "\[Delta]"}]]}], "=", 
     RowBox[{
      RowBox[{
       RowBox[{"-", 
        RowBox[{"log", "(", "\[Delta]", ")"}]}], "+", 
       RowBox[{"log", "(", "1", ")"}]}], "\[Implies]", "0."}]}], " "}], 
   TraditionalForm]]]
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{"1", "/", 
    RowBox[{"(", 
     RowBox[{"1", "-", "x"}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[6]:=",
 CellID->1084770727],

Cell[BoxData[
 FormBox["0", TraditionalForm]], "Output",
 ImageSize->{13, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[6]="]
}, Open  ]],

Cell[TextData[{
 "In the physics literature sometimes the \"+\" notation is used. In FeynCalc \
the ",
 Cell[BoxData[
  FormBox[
   SubscriptBox[
    RowBox[{"(", 
     FractionBox["1", 
      RowBox[{"1", "-", "x"}]], ")"}], "+"], TraditionalForm]]],
 " is represented by ",
 Cell[BoxData[
  FormBox[
   RowBox[{"PlusDistribution", "[", 
    RowBox[{"1", "/", 
     RowBox[{"(", 
      RowBox[{"1", "-", "x"}], ")"}]}], "]"}], TraditionalForm]]],
 " or just ",
 Cell[BoxData[
  FormBox[
   RowBox[{"1", "/", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "-", "x"}], ")"}], " ", "."}]}], TraditionalForm]]]
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{"PlusDistribution", "[", 
    RowBox[{"1", "/", 
     RowBox[{"(", 
      RowBox[{"1", "-", "x"}], ")"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[7]:=",
 CellID->1725124689],

Cell[BoxData[
 FormBox["0", TraditionalForm]], "Output",
 ImageSize->{13, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[7]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"PolyLog", "[", 
     RowBox[{"2", ",", 
      RowBox[{"1", "-", "x"}]}], "]"}], "/", 
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "-", "x"}], ")"}], "^", "2"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[8]:=",
 CellID->1940746510],

Cell[BoxData[
 FormBox[
  RowBox[{"2", "-", 
   RowBox[{"\[Zeta]", "(", "2", ")"}]}], TraditionalForm]], "Output",
 ImageSize->{59, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[8]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"Log", "[", "x", "]"}], " ", 
      RowBox[{"Log", "[", 
       RowBox[{"1", "+", "x"}], "]"}]}], ")"}], "/", 
    RowBox[{"(", 
     RowBox[{"1", "+", "x"}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[9]:=",
 CellID->582396558],

Cell[BoxData[
 FormBox[
  RowBox[{"-", 
   FractionBox[
    TemplateBox[{"3"},
     "Zeta"], "8"]}], TraditionalForm]], "Output",
 ImageSize->{48, 34},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[9]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"Log", "[", "x", "]"}], "^", "2"}], "/", 
    RowBox[{"(", 
     RowBox[{"1", "-", "x"}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[10]:=",
 CellID->845490247],

Cell[BoxData[
 FormBox[
  RowBox[{"2", " ", 
   TemplateBox[{"3"},
    "Zeta"]}], TraditionalForm]], "Output",
 ImageSize->{45, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[10]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"PolyLog", "[", 
     RowBox[{"2", ",", 
      RowBox[{"-", "x"}]}], "]"}], "/", 
    RowBox[{"(", 
     RowBox[{"1", "+", "x"}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[11]:=",
 CellID->1121674397],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    TemplateBox[{"3"},
     "Zeta"], "4"], "-", 
   RowBox[{
    FractionBox["1", "2"], " ", 
    RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
    RowBox[{"log", "(", "2", ")"}]}]}], TraditionalForm]], "Output",
 ImageSize->{143, 35},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[11]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"Log", "[", "x", "]"}], " ", 
    RowBox[{"PolyLog", "[", 
     RowBox[{"2", ",", "x"}], "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[12]:=",
 CellID->1584122311],

Cell[BoxData[
 FormBox[
  RowBox[{"3", "-", 
   RowBox[{"2", " ", 
    RowBox[{"\[Zeta]", "(", "2", ")"}]}]}], TraditionalForm]], "Output",
 ImageSize->{70, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[12]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{"x", " ", 
    RowBox[{"PolyLog", "[", 
     RowBox[{"3", ",", "x"}], "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[13]:=",
 CellID->1907301251],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     RowBox[{"\[Zeta]", "(", "2", ")"}], "4"]}], "+", 
   FractionBox[
    TemplateBox[{"3"},
     "Zeta"], "2"], "+", 
   FractionBox["3", "16"]}], TraditionalForm]], "Output",
 ImageSize->{133, 34},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[13]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{
       RowBox[{"Log", "[", "x", "]"}], "^", "2"}], " ", 
      RowBox[{"Log", "[", 
       RowBox[{"1", "-", "x"}], "]"}]}], ")"}], "/", 
    RowBox[{"(", 
     RowBox[{"1", "+", "x"}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[14]:=",
 CellID->1237143526],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"\[Zeta]", "(", "4", ")"}], "+", 
   RowBox[{
    RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
    RowBox[{
     SuperscriptBox["log", "2"], "(", "2", ")"}]}], "-", 
   RowBox[{"4", " ", 
    TemplateBox[{"4",FractionBox["1", "2"]},
     "PolyLog"]}], "-", 
   FractionBox[
    RowBox[{
     SuperscriptBox["log", "4"], "(", "2", ")"}], "6"]}], 
  TraditionalForm]], "Output",
 ImageSize->{275, 39},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[14]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"PolyLog", "[", 
     RowBox[{"2", ",", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           RowBox[{"x", " ", 
            RowBox[{"(", 
             RowBox[{"1", "-", "z"}], ")"}]}], "+", "z"}], ")"}], " ", 
         RowBox[{"(", 
          RowBox[{"1", "-", "x", "+", 
           RowBox[{"x", " ", "z"}]}], ")"}]}], ")"}], "/", "z"}]}], "]"}], 
    "/", 
    RowBox[{"(", 
     RowBox[{"1", "-", "x", "+", 
      RowBox[{"x", " ", "z"}]}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[15]:=",
 CellID->2080558124],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", 
     TemplateBox[{"2",RowBox[{"-", "z"}]},
      "PolyLog"]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{"4", " ", 
     TemplateBox[{"3",FractionBox[
        RowBox[{"1", "-", "z"}], "2"]},
      "PolyLog"]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     TemplateBox[{"3",RowBox[{"1", "-", "z"}]},
      "PolyLog"]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"2", " ", 
     TemplateBox[{"3",RowBox[{"-", "z"}]},
      "PolyLog"]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     TemplateBox[{"3",FractionBox["1", 
        RowBox[{"z", "+", "1"}]]},
      "PolyLog"]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{"4", " ", 
     TemplateBox[{"3",FractionBox[
        RowBox[{"1", "-", "z"}], 
        RowBox[{"z", "+", "1"}]]},
      "PolyLog"]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{"4", " ", 
     TemplateBox[{"3",FractionBox[
        RowBox[{"z", "+", "1"}], "2"]},
      "PolyLog"]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{"2", " ", 
     TemplateBox[{"2",RowBox[{"1", "-", "z"}]},
      "PolyLog"], " ", 
     RowBox[{"log", "(", "z", ")"}]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{"2", " ", 
     TemplateBox[{"2",RowBox[{"-", "z"}]},
      "PolyLog"], " ", 
     RowBox[{"log", "(", "z", ")"}]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     TemplateBox[{"2",RowBox[{"-", "z"}]},
      "PolyLog"], " ", 
     RowBox[{"log", "(", 
      RowBox[{"1", "-", "z"}], ")"}]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{"2", " ", 
     RowBox[{
      SubscriptBox["S", 
       RowBox[{
        FormBox["1",
         TraditionalForm], 
        FormBox["2",
         TraditionalForm]}]], "(", 
      FormBox[
       RowBox[{"1", "-", "z"}],
       TraditionalForm], ")"}]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"\[ImaginaryI]", " ", "\[Pi]", " ", 
     RowBox[{"\[Zeta]", "(", "2", ")"}]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     RowBox[{"log", "(", "z", ")"}]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"2", " ", 
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"1", "-", "z"}], ")"}]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"6", " ", 
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"z", "+", "1"}], ")"}]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{"4", " ", 
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     RowBox[{"log", "(", "2", ")"}]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"2", " ", 
     TemplateBox[{"3"},
      "Zeta"]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox["log", "3"], "(", "z", ")"}], 
    RowBox[{"6", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "z"}], ")"}]}]], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     RowBox[{
      SuperscriptBox["log", "3"], "(", "2", ")"}]}], 
    RowBox[{"3", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "z"}], ")"}]}]], "-", 
   FractionBox[
    RowBox[{
     RowBox[{"log", "(", 
      RowBox[{"1", "-", "z"}], ")"}], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "z", ")"}]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{
     RowBox[{"log", "(", 
      RowBox[{"z", "+", "1"}], ")"}], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "z", ")"}]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{"\[ImaginaryI]", " ", "\[Pi]", " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "z", ")"}]}], 
    RowBox[{"2", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "z"}], ")"}]}]], "-", 
   FractionBox[
    RowBox[{"2", " ", 
     RowBox[{"log", "(", 
      RowBox[{"1", "-", "z"}], ")"}], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", 
      RowBox[{"z", "+", "1"}], ")"}]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{"2", " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "2", ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"1", "-", "z"}], ")"}]}], 
    RowBox[{"1", "-", "z"}]], "-", 
   FractionBox[
    RowBox[{"2", " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "2", ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"z", "+", "1"}], ")"}]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     RowBox[{"log", "(", 
      RowBox[{"1", "-", "z"}], ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"z", "+", "1"}], ")"}], " ", 
     RowBox[{"log", "(", "z", ")"}]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", 
     RowBox[{"log", "(", 
      RowBox[{"z", "+", "1"}], ")"}], " ", 
     RowBox[{"log", "(", "z", ")"}]}], 
    RowBox[{"1", "-", "z"}]], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     RowBox[{"log", "(", "2", ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"1", "-", "z"}], ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"z", "+", "1"}], ")"}]}], 
    RowBox[{"1", "-", "z"}]]}], TraditionalForm]], "Output",
 ImageSize->{564, 351},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[15]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Apart", "[", 
  RowBox[{
   RowBox[{"Integrate2", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"x", "^", 
       RowBox[{"(", 
        RowBox[{"OPEm", "-", "1"}], ")"}]}], " ", 
      RowBox[{"PolyLog", "[", 
       RowBox[{"3", ",", 
        RowBox[{"1", "-", "x"}]}], "]"}]}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], ",", "OPEm"}], 
  "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[16]:=",
 CellID->204763000],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     RowBox[{"\[Zeta]", "(", "2", ")"}], 
     SuperscriptBox["m", "2"]]}], "-", 
   FractionBox[
    RowBox[{"\[Zeta]", "(", "2", ")"}], 
    RowBox[{"m", "-", "1"}]], "+", 
   FractionBox[
    RowBox[{
     RowBox[{"\[Zeta]", "(", "2", ")"}], "+", 
     RowBox[{
      RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
      RowBox[{"(", 
       RowBox[{"-", 
        RowBox[{
         SubscriptBox["S", "1"], "(", 
         FormBox[
          RowBox[{"m", "-", "2"}],
          TraditionalForm], ")"}]}], ")"}]}], "+", 
     RowBox[{
      SubscriptBox["S", "12"], "(", 
      FormBox["m",
       TraditionalForm], ")"}], "+", 
     TemplateBox[{"3"},
      "Zeta"]}], "m"]}], TraditionalForm]], "Output",
 ImageSize->{404, 35},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[16]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Integrate2", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"x", "^", 
      RowBox[{"(", 
       RowBox[{"OPEm", "-", "1"}], ")"}]}], " ", 
     RowBox[{"Log", "[", 
      RowBox[{"1", "-", "x"}], "]"}], " ", 
     RowBox[{"Log", "[", "x", "]"}], " ", 
     FractionBox[
      RowBox[{"Log", "[", 
       RowBox[{"1", "+", "x"}], "]"}], 
      RowBox[{"1", "+", "x"}]]}], ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], "//", 
  "Simplify"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[17]:=",
 CellID->1234589200],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox["1", "24"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     RowBox[{"-", "1"}], ")"}], "m"], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"48", " ", 
      RowBox[{"\[Zeta]", "(", "4", ")"}]}], "+", 
     RowBox[{"30", " ", 
      RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
      RowBox[{
       SuperscriptBox["log", "2"], "(", "2", ")"}]}], "+", 
     RowBox[{"6", " ", 
      RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
      RowBox[{
       SubsuperscriptBox["S", 
        RowBox[{"-", "1"}], "2"], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "+", 
     RowBox[{"18", " ", 
      RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
      RowBox[{
       SubscriptBox["S", "2"], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "-", 
     RowBox[{"24", " ", 
      RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{"1", "-", "1"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "-", 
     RowBox[{"12", " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{"-", "2"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"\[Zeta]", "(", "2", ")"}], "-", 
        RowBox[{
         RowBox[{"log", "(", "4", ")"}], " ", 
         RowBox[{
          SubscriptBox["S", 
           RowBox[{"-", "1"}]], "(", 
          FormBox[
           RowBox[{"m", "-", "1"}],
           TraditionalForm], ")"}]}], "-", 
        RowBox[{
         SuperscriptBox["log", "2"], "(", "2", ")"}]}], ")"}]}], "-", 
     RowBox[{"36", " ", 
      RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
      RowBox[{"log", "(", "2", ")"}], " ", 
      RowBox[{
       SubscriptBox["S", "1"], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "+", 
     RowBox[{"12", " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{"-", "1"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
         RowBox[{"log", "(", "8", ")"}]}], "-", 
        RowBox[{"2", " ", 
         TemplateBox[{"3"},
          "Zeta"]}]}], ")"}]}], "+", 
     RowBox[{"39", " ", 
      TemplateBox[{"3"},
       "Zeta"], " ", 
      RowBox[{
       SubscriptBox["S", "1"], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "+", 
     RowBox[{"24", " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{
         RowBox[{"-", "2"}], "-", "1", "-", "1"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "+", 
     RowBox[{"24", " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{
         RowBox[{"-", "1"}], "-", "2", "-", "1"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "+", 
     RowBox[{"24", " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{
         RowBox[{"-", "1"}], "-", "1", "-", "2"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "+", 
     RowBox[{"24", " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{"1", "-", "21"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "+", 
     RowBox[{"24", " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{"1", "-", "12"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "+", 
     RowBox[{"24", " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{"2", "-", "11"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "-", 
     RowBox[{"12", " ", 
      RowBox[{
       SuperscriptBox["log", "2"], "(", "2", ")"}], " ", 
      RowBox[{
       SubscriptBox["S", "2"], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "+", 
     RowBox[{"24", " ", 
      RowBox[{"log", "(", "2", ")"}], " ", 
      RowBox[{
       SubscriptBox["S", "3"], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "-", 
     RowBox[{"24", " ", 
      RowBox[{"log", "(", "2", ")"}], " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{"-", "21"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "-", 
     RowBox[{"24", " ", 
      RowBox[{"log", "(", "2", ")"}], " ", 
      RowBox[{
       SubscriptBox["S", 
        RowBox[{"-", "12"}]], "(", 
       FormBox[
        RowBox[{"m", "-", "1"}],
        TraditionalForm], ")"}]}], "-", 
     RowBox[{"48", " ", 
      TemplateBox[{"4",FractionBox["1", "2"]},
       "PolyLog"]}], "-", 
     RowBox[{"63", " ", 
      TemplateBox[{"3"},
       "Zeta"], " ", 
      RowBox[{"log", "(", "2", ")"}]}], "-", 
     RowBox[{"2", " ", 
      RowBox[{
       SuperscriptBox["log", "4"], "(", "2", ")"}]}]}], ")"}]}], 
  TraditionalForm]], "Output",
 ImageSize->{530, 185},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[17]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"%", " ", "/.", " ", 
  RowBox[{"OPEm", "\[Rule]", "2"}]}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[18]:=",
 CellID->1839623139],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox["1", "24"], " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"48", " ", 
      RowBox[{"\[Zeta]", "(", "2", ")"}]}], "+", 
     RowBox[{"48", " ", 
      RowBox[{"\[Zeta]", "(", "4", ")"}]}], "+", 
     RowBox[{"30", " ", 
      RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
      RowBox[{
       SuperscriptBox["log", "2"], "(", "2", ")"}]}], "+", 
     RowBox[{"12", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{"\[Zeta]", "(", "2", ")"}], "-", 
        RowBox[{
         SuperscriptBox["log", "2"], "(", "2", ")"}], "+", 
        RowBox[{"log", "(", "4", ")"}]}], ")"}]}], "-", 
     RowBox[{"36", " ", 
      RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
      RowBox[{"log", "(", "2", ")"}]}], "-", 
     RowBox[{"48", " ", 
      TemplateBox[{"4",FractionBox["1", "2"]},
       "PolyLog"]}], "-", 
     RowBox[{"12", " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
         RowBox[{"log", "(", "8", ")"}]}], "-", 
        RowBox[{"2", " ", 
         TemplateBox[{"3"},
          "Zeta"]}]}], ")"}]}], "+", 
     RowBox[{"39", " ", 
      TemplateBox[{"3"},
       "Zeta"]}], "-", 
     RowBox[{"63", " ", 
      TemplateBox[{"3"},
       "Zeta"], " ", 
      RowBox[{"log", "(", "2", ")"}]}], "-", "144", "-", 
     RowBox[{"2", " ", 
      RowBox[{
       SuperscriptBox["log", "4"], "(", "2", ")"}]}], "-", 
     RowBox[{"12", " ", 
      RowBox[{
       SuperscriptBox["log", "2"], "(", "2", ")"}]}], "+", 
     RowBox[{"72", " ", 
      RowBox[{"log", "(", "2", ")"}]}]}], ")"}]}], TraditionalForm]], "Output",\

 ImageSize->{472, 118},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[18]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "[", "%", "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[19]:=",
 CellID->1653791497],

Cell[BoxData[
 FormBox["0.050513835402744935`", TraditionalForm]], "Output",
 ImageSize->{64, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[19]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"x", "^", 
     RowBox[{"(", 
      RowBox[{"OPEm", "-", "1"}], ")"}]}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"PolyLog", "[", 
       RowBox[{"3", ",", 
        FractionBox[
         RowBox[{"1", "-", "x"}], 
         RowBox[{"1", "+", "x"}]]}], "]"}], "-", 
      RowBox[{"PolyLog", "[", 
       RowBox[{"3", ",", 
        RowBox[{"-", 
         FractionBox[
          RowBox[{"1", "-", "x"}], 
          RowBox[{"1", "+", "x"}]]}]}], "]"}]}], ")"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[20]:=",
 CellID->1526670238],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"3", " ", 
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{"log", "(", "2", ")"}]}], 
    RowBox[{"2", " ", "m"}]], "-", 
   FractionBox[
    RowBox[{"3", " ", 
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     RowBox[{"log", "(", "2", ")"}]}], 
    RowBox[{"2", " ", "m"}]], "+", 
   FractionBox[
    RowBox[{
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{
      SubscriptBox["S", 
       RowBox[{"-", "1"}]], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "-", 
   FractionBox[
    RowBox[{
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     RowBox[{
      SubscriptBox["S", 
       RowBox[{"-", "1"}]], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], 
    RowBox[{"2", " ", "m"}]], "+", 
   FractionBox[
    RowBox[{
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], 
    RowBox[{"2", " ", "m"}]], "-", 
   FractionBox[
    RowBox[{
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{
      SubscriptBox["S", 
       RowBox[{"-", "3"}]], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{
      SubscriptBox["S", 
       RowBox[{"-", "2"}]], "(", 
      FormBox["m",
       TraditionalForm], ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox["m",
       TraditionalForm], ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "2"], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     SubscriptBox["S", "3"], "(", 
     FormBox["m",
      TraditionalForm], ")"}], "m"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], 
      RowBox[{"m", "+", "1"}]], " ", 
     RowBox[{
      SubscriptBox["S", 
       RowBox[{"-", "21"}]], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "-", 
   FractionBox[
    RowBox[{
     SubscriptBox["S", 
      RowBox[{
       RowBox[{"-", "1"}], "-", "2"}]], "(", 
     FormBox["m",
      TraditionalForm], ")"}], "m"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], 
      RowBox[{"m", "+", "1"}]], " ", 
     RowBox[{
      SubscriptBox["S", 
       RowBox[{"-", "12"}]], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "-", 
   FractionBox[
    RowBox[{
     SubscriptBox["S", "21"], "(", 
     FormBox["m",
      TraditionalForm], ")"}], "m"], "-", 
   FractionBox[
    RowBox[{"7", " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     TemplateBox[{"3"},
      "Zeta"]}], 
    RowBox[{"8", " ", "m"}]], "+", 
   FractionBox[
    RowBox[{"21", " ", 
     TemplateBox[{"3"},
      "Zeta"]}], 
    RowBox[{"8", " ", "m"}]]}], TraditionalForm]], "Output",
 ImageSize->{481, 173},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[20]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DataType", "[", 
  RowBox[{"OPEm", ",", "PositiveInteger"}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[21]:=",
 CellID->20428829],

Cell[BoxData[
 FormBox["True", TraditionalForm]], "Output",
 ImageSize->{31, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[21]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"x", "^", 
     RowBox[{"(", 
      RowBox[{"OPEm", "-", "1"}], ")"}]}], " ", 
    RowBox[{"DeltaFunction", "[", 
     RowBox[{"1", "-", "x"}], "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[22]:=",
 CellID->512808203],

Cell[BoxData[
 FormBox["1", TraditionalForm]], "Output",
 ImageSize->{11, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[22]="]
}, Open  ]],

Cell["\<\
This is the polarized non-singlet spin splitting function whose first moment \
vanishes.\
\>", "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"t", "=", 
  RowBox[{
   RowBox[{"SplittingFunction", "[", "PQQNS", "]"}], "/.", 
   RowBox[{
    RowBox[{"FCGV", "[", "z_", "]"}], "\[RuleDelayed]", 
    RowBox[{"ToExpression", "[", "z", "]"}]}]}]}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[23]:=",
 CellID->18981591],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{
    RowBox[{"-", "8"}], " ", 
    SubscriptBox["C", "F"], " ", 
    RowBox[{"(", 
     RowBox[{
      SubscriptBox["C", "F"], "-", 
      FractionBox[
       SubscriptBox["C", "A"], "2"]}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{
      FractionBox[
       RowBox[{
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["x", "2"], "+", "1"}], ")"}], " ", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"-", 
           RowBox[{"2", " ", 
            RowBox[{"\[Zeta]", "(", "2", ")"}]}]}], "-", 
          RowBox[{"4", " ", 
           TemplateBox[{"2",RowBox[{"-", "x"}]},
            "PolyLog"]}], "+", 
          RowBox[{
           SuperscriptBox["log", "2"], "(", "x", ")"}], "-", 
          RowBox[{"4", " ", 
           RowBox[{"log", "(", 
            RowBox[{"x", "+", "1"}], ")"}], " ", 
           RowBox[{"log", "(", "x", ")"}]}]}], ")"}]}], 
       RowBox[{"x", "+", "1"}]], "+", 
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"1", "-", "x"}], ")"}]}], "+", 
      RowBox[{"2", " ", 
       RowBox[{"(", 
        RowBox[{"x", "+", "1"}], ")"}], " ", 
       RowBox[{"log", "(", "x", ")"}]}]}], ")"}]}], "+", 
   RowBox[{
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"], " ", 
    RowBox[{"(", 
     RowBox[{
      FractionBox[
       RowBox[{"4", " ", 
        RowBox[{"(", 
         RowBox[{
          SuperscriptBox["x", "2"], "+", "1"}], ")"}], " ", 
        RowBox[{
         SuperscriptBox["log", "2"], "(", "x", ")"}]}], 
       RowBox[{"1", "-", "x"}]], "+", 
      RowBox[{"8", " ", 
       RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
       RowBox[{"(", 
        RowBox[{"x", "+", "1"}], ")"}]}], "+", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         FractionBox["536", "9"], "-", 
         RowBox[{"16", " ", 
          RowBox[{"\[Zeta]", "(", "2", ")"}]}]}], ")"}], " ", 
       SubscriptBox[
        RowBox[{"(", 
         FractionBox["1", 
          RowBox[{"1", "-", "x"}]], ")"}], "+"]}], "+", 
      RowBox[{
       RowBox[{"\[Delta]", "(", 
        FormBox[
         RowBox[{"1", "-", "x"}],
         TraditionalForm], ")"}], " ", 
       RowBox[{"(", 
        RowBox[{
         FractionBox[
          RowBox[{"88", " ", 
           RowBox[{"\[Zeta]", "(", "2", ")"}]}], "3"], "-", 
         RowBox[{"24", " ", 
          TemplateBox[{"3"},
           "Zeta"]}], "+", 
         FractionBox["17", "3"]}], ")"}]}], "+", 
      RowBox[{
       FractionBox["4", "9"], " ", 
       RowBox[{"(", 
        RowBox[{"53", "-", 
         RowBox[{"187", " ", "x"}]}], ")"}]}], "-", 
      RowBox[{
       FractionBox["4", "3"], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"5", " ", "x"}], "-", 
         FractionBox["22", 
          RowBox[{"1", "-", "x"}]], "+", "5"}], ")"}], " ", 
       RowBox[{"log", "(", "x", ")"}]}]}], ")"}]}], "+", 
   RowBox[{
    SubscriptBox["C", "F"], " ", 
    SubscriptBox["N", "f"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       FractionBox[
        RowBox[{"8", " ", 
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox["x", "2"], "+", "1"}], ")"}], " ", 
         RowBox[{"log", "(", "x", ")"}]}], 
        RowBox[{"3", " ", 
         RowBox[{"(", 
          RowBox[{"1", "-", "x"}], ")"}]}]]}], "+", 
      RowBox[{
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", 
          FractionBox[
           RowBox[{"16", " ", 
            RowBox[{"\[Zeta]", "(", "2", ")"}]}], "3"]}], "-", 
         FractionBox["2", "3"]}], ")"}], " ", 
       RowBox[{"\[Delta]", "(", 
        FormBox[
         RowBox[{"1", "-", "x"}],
         TraditionalForm], ")"}]}], "+", 
      FractionBox[
       RowBox[{"88", " ", "x"}], "9"], "-", 
      RowBox[{
       FractionBox["80", "9"], " ", 
       SubscriptBox[
        RowBox[{"(", 
         FractionBox["1", 
          RowBox[{"1", "-", "x"}]], ")"}], "+"]}], "-", 
      FractionBox["8", "9"]}], ")"}]}], "+", 
   RowBox[{
    SubsuperscriptBox["C", "F", "2"], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       FractionBox[
        RowBox[{"16", " ", 
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox["x", "2"], "+", "1"}], ")"}], " ", 
         RowBox[{"log", "(", 
          RowBox[{"1", "-", "x"}], ")"}], " ", 
         RowBox[{"log", "(", "x", ")"}]}], 
        RowBox[{"1", "-", "x"}]]}], "+", 
      RowBox[{
       RowBox[{"\[Delta]", "(", 
        FormBox[
         RowBox[{"1", "-", "x"}],
         TraditionalForm], ")"}], " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"-", 
          RowBox[{"24", " ", 
           RowBox[{"\[Zeta]", "(", "2", ")"}]}]}], "+", 
         RowBox[{"48", " ", 
          TemplateBox[{"3"},
           "Zeta"]}], "+", "3"}], ")"}]}], "-", 
      RowBox[{"40", " ", 
       RowBox[{"(", 
        RowBox[{"1", "-", "x"}], ")"}]}], "-", 
      RowBox[{"4", " ", 
       RowBox[{"(", 
        RowBox[{"x", "+", "1"}], ")"}], " ", 
       RowBox[{
        SuperscriptBox["log", "2"], "(", "x", ")"}]}], "-", 
      RowBox[{"8", " ", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"2", " ", "x"}], "+", 
         FractionBox["3", 
          RowBox[{"1", "-", "x"}]]}], ")"}], " ", 
       RowBox[{"log", "(", "x", ")"}]}]}], ")"}]}]}], 
  TraditionalForm]], "Output",
 ImageSize->{575, 373},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[23]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"t", "//", "Expand"}]], "Input",
 CellLabel->"In[24]:="],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"8", " ", 
    RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"]}], "-", 
   FractionBox[
    RowBox[{"16", " ", 
     SuperscriptBox["x", "2"], " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"], " ", 
     TemplateBox[{"2",RowBox[{"-", "x"}]},
      "PolyLog"]}], 
    RowBox[{"x", "+", "1"}]], "-", 
   FractionBox[
    RowBox[{"16", " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"], " ", 
     TemplateBox[{"2",RowBox[{"-", "x"}]},
      "PolyLog"]}], 
    RowBox[{"x", "+", "1"}]], "-", 
   FractionBox[
    RowBox[{"8", " ", 
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     SuperscriptBox["x", "2"], " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"]}], 
    RowBox[{"x", "+", "1"}]], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     SuperscriptBox["x", "2"], " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "x", ")"}]}], 
    RowBox[{"1", "-", "x"}]], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     SuperscriptBox["x", "2"], " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "x", ")"}]}], 
    RowBox[{"x", "+", "1"}]], "-", 
   FractionBox[
    RowBox[{"16", " ", 
     SuperscriptBox["x", "2"], " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"], " ", 
     RowBox[{"log", "(", "x", ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"x", "+", "1"}], ")"}]}], 
    RowBox[{"x", "+", "1"}]], "+", 
   RowBox[{
    FractionBox["88", "3"], " ", 
    RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"], " ", 
    RowBox[{"\[Delta]", "(", 
     FormBox[
      RowBox[{"1", "-", "x"}],
      TraditionalForm], ")"}]}], "+", 
   RowBox[{
    FractionBox["17", "3"], " ", 
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"], " ", 
    RowBox[{"\[Delta]", "(", 
     FormBox[
      RowBox[{"1", "-", "x"}],
      TraditionalForm], ")"}]}], "+", 
   RowBox[{"8", " ", 
    RowBox[{"\[Zeta]", "(", "2", ")"}], " ", "x", " ", 
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"]}], "-", 
   FractionBox[
    RowBox[{"8", " ", 
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"]}], 
    RowBox[{"x", "+", "1"}]], "-", 
   RowBox[{"16", " ", 
    RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
    SubscriptBox[
     RowBox[{"(", 
      FractionBox["1", 
       RowBox[{"1", "-", "x"}]], ")"}], "+"], " ", 
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"]}], "-", 
   RowBox[{"24", " ", 
    TemplateBox[{"3"},
     "Zeta"], " ", 
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"], " ", 
    RowBox[{"\[Delta]", "(", 
     FormBox[
      RowBox[{"1", "-", "x"}],
      TraditionalForm], ")"}]}], "-", 
   RowBox[{
    FractionBox["892", "9"], " ", "x", " ", 
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"]}], "+", 
   RowBox[{
    FractionBox["536", "9"], " ", 
    SubscriptBox[
     RowBox[{"(", 
      FractionBox["1", 
       RowBox[{"1", "-", "x"}]], ")"}], "+"], " ", 
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"]}], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "x", ")"}]}], 
    RowBox[{"1", "-", "x"}]], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "x", ")"}]}], 
    RowBox[{"x", "+", "1"}]], "+", 
   RowBox[{
    FractionBox["4", "3"], " ", 
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"], " ", 
    RowBox[{"log", "(", "x", ")"}]}], "+", 
   RowBox[{
    FractionBox["4", "3"], " ", "x", " ", 
    SubscriptBox["C", "A"], " ", 
    SubscriptBox["C", "F"], " ", 
    RowBox[{"log", "(", "x", ")"}]}], "+", 
   FractionBox[
    RowBox[{"88", " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"], " ", 
     RowBox[{"log", "(", "x", ")"}]}], 
    RowBox[{"3", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "x"}], ")"}]}]], "-", 
   FractionBox[
    RowBox[{"16", " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"], " ", 
     RowBox[{"log", "(", "x", ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"x", "+", "1"}], ")"}]}], 
    RowBox[{"x", "+", "1"}]], "+", 
   FractionBox[
    RowBox[{"356", " ", 
     SubscriptBox["C", "A"], " ", 
     SubscriptBox["C", "F"]}], "9"], "-", 
   FractionBox[
    RowBox[{"8", " ", 
     SuperscriptBox["x", "2"], " ", 
     SubscriptBox["C", "F"], " ", 
     SubscriptBox["N", "f"], " ", 
     RowBox[{"log", "(", "x", ")"}]}], 
    RowBox[{"3", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "x"}], ")"}]}]], "-", 
   RowBox[{
    FractionBox["16", "3"], " ", 
    RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
    SubscriptBox["C", "F"], " ", 
    SubscriptBox["N", "f"], " ", 
    RowBox[{"\[Delta]", "(", 
     FormBox[
      RowBox[{"1", "-", "x"}],
      TraditionalForm], ")"}]}], "-", 
   RowBox[{
    FractionBox["2", "3"], " ", 
    SubscriptBox["C", "F"], " ", 
    SubscriptBox["N", "f"], " ", 
    RowBox[{"\[Delta]", "(", 
     FormBox[
      RowBox[{"1", "-", "x"}],
      TraditionalForm], ")"}]}], "+", 
   RowBox[{
    FractionBox["88", "9"], " ", "x", " ", 
    SubscriptBox["C", "F"], " ", 
    SubscriptBox["N", "f"]}], "-", 
   RowBox[{
    FractionBox["80", "9"], " ", 
    SubscriptBox[
     RowBox[{"(", 
      FractionBox["1", 
       RowBox[{"1", "-", "x"}]], ")"}], "+"], " ", 
    SubscriptBox["C", "F"], " ", 
    SubscriptBox["N", "f"]}], "-", 
   FractionBox[
    RowBox[{"8", " ", 
     SubscriptBox["C", "F"], " ", 
     SubscriptBox["N", "f"], " ", 
     RowBox[{"log", "(", "x", ")"}]}], 
    RowBox[{"3", " ", 
     RowBox[{"(", 
      RowBox[{"1", "-", "x"}], ")"}]}]], "-", 
   FractionBox[
    RowBox[{"8", " ", 
     SubscriptBox["C", "F"], " ", 
     SubscriptBox["N", "f"]}], "9"], "+", 
   FractionBox[
    RowBox[{"32", " ", 
     SuperscriptBox["x", "2"], " ", 
     SubsuperscriptBox["C", "F", "2"], " ", 
     TemplateBox[{"2",RowBox[{"-", "x"}]},
      "PolyLog"]}], 
    RowBox[{"x", "+", "1"}]], "+", 
   FractionBox[
    RowBox[{"32", " ", 
     SubsuperscriptBox["C", "F", "2"], " ", 
     TemplateBox[{"2",RowBox[{"-", "x"}]},
      "PolyLog"]}], 
    RowBox[{"x", "+", "1"}]], "+", 
   FractionBox[
    RowBox[{"16", " ", 
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     SuperscriptBox["x", "2"], " ", 
     SubsuperscriptBox["C", "F", "2"]}], 
    RowBox[{"x", "+", "1"}]], "-", 
   FractionBox[
    RowBox[{"8", " ", 
     SuperscriptBox["x", "2"], " ", 
     SubsuperscriptBox["C", "F", "2"], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "x", ")"}]}], 
    RowBox[{"x", "+", "1"}]], "-", 
   FractionBox[
    RowBox[{"16", " ", 
     SuperscriptBox["x", "2"], " ", 
     SubsuperscriptBox["C", "F", "2"], " ", 
     RowBox[{"log", "(", 
      RowBox[{"1", "-", "x"}], ")"}], " ", 
     RowBox[{"log", "(", "x", ")"}]}], 
    RowBox[{"1", "-", "x"}]], "+", 
   FractionBox[
    RowBox[{"32", " ", 
     SuperscriptBox["x", "2"], " ", 
     SubsuperscriptBox["C", "F", "2"], " ", 
     RowBox[{"log", "(", "x", ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"x", "+", "1"}], ")"}]}], 
    RowBox[{"x", "+", "1"}]], "-", 
   RowBox[{"24", " ", 
    RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
    SubsuperscriptBox["C", "F", "2"], " ", 
    RowBox[{"\[Delta]", "(", 
     FormBox[
      RowBox[{"1", "-", "x"}],
      TraditionalForm], ")"}]}], "+", 
   RowBox[{"3", " ", 
    SubsuperscriptBox["C", "F", "2"], " ", 
    RowBox[{"\[Delta]", "(", 
     FormBox[
      RowBox[{"1", "-", "x"}],
      TraditionalForm], ")"}]}], "+", 
   FractionBox[
    RowBox[{"16", " ", 
     RowBox[{"\[Zeta]", "(", "2", ")"}], " ", 
     SubsuperscriptBox["C", "F", "2"]}], 
    RowBox[{"x", "+", "1"}]], "+", 
   RowBox[{"48", " ", 
    TemplateBox[{"3"},
     "Zeta"], " ", 
    SubsuperscriptBox["C", "F", "2"], " ", 
    RowBox[{"\[Delta]", "(", 
     FormBox[
      RowBox[{"1", "-", "x"}],
      TraditionalForm], ")"}]}], "+", 
   RowBox[{"72", " ", "x", " ", 
    SubsuperscriptBox["C", "F", "2"]}], "-", 
   RowBox[{"4", " ", "x", " ", 
    SubsuperscriptBox["C", "F", "2"], " ", 
    RowBox[{
     SuperscriptBox["log", "2"], "(", "x", ")"}]}], "-", 
   FractionBox[
    RowBox[{"8", " ", 
     SubsuperscriptBox["C", "F", "2"], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "x", ")"}]}], 
    RowBox[{"x", "+", "1"}]], "-", 
   RowBox[{"4", " ", 
    SubsuperscriptBox["C", "F", "2"], " ", 
    RowBox[{
     SuperscriptBox["log", "2"], "(", "x", ")"}]}], "-", 
   RowBox[{"32", " ", "x", " ", 
    SubsuperscriptBox["C", "F", "2"], " ", 
    RowBox[{"log", "(", "x", ")"}]}], "-", 
   FractionBox[
    RowBox[{"16", " ", 
     SubsuperscriptBox["C", "F", "2"], " ", 
     RowBox[{"log", "(", 
      RowBox[{"1", "-", "x"}], ")"}], " ", 
     RowBox[{"log", "(", "x", ")"}]}], 
    RowBox[{"1", "-", "x"}]], "-", 
   FractionBox[
    RowBox[{"24", " ", 
     SubsuperscriptBox["C", "F", "2"], " ", 
     RowBox[{"log", "(", "x", ")"}]}], 
    RowBox[{"1", "-", "x"}]], "-", 
   RowBox[{"16", " ", 
    SubsuperscriptBox["C", "F", "2"], " ", 
    RowBox[{"log", "(", "x", ")"}]}], "+", 
   FractionBox[
    RowBox[{"32", " ", 
     SubsuperscriptBox["C", "F", "2"], " ", 
     RowBox[{"log", "(", "x", ")"}], " ", 
     RowBox[{"log", "(", 
      RowBox[{"x", "+", "1"}], ")"}]}], 
    RowBox[{"x", "+", "1"}]], "-", 
   RowBox[{"72", " ", 
    SubsuperscriptBox["C", "F", "2"]}]}], TraditionalForm]], "Output",
 ImageSize->{570, 584},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[24]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"Integrate2", "[", 
   RowBox[{"t", ",", 
    RowBox[{"{", 
     RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], "//", 
  "Timing"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[25]:=",
 CellID->182134904],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{"0.047429`", ",", "0"}], "}"}], TraditionalForm]], "Output",
 ImageSize->{88, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[25]="]
}, Open  ]],

Cell["\<\
Expanding t with respect to x yields a form already suitable for Integrate3 \
and therefore the following is faster:\
\>", "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"Integrate3", "[", 
    RowBox[{
     RowBox[{"Expand", "[", 
      RowBox[{"t", ",", "x"}], "]"}], ",", 
     RowBox[{"{", 
      RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}], "//", "Expand"}], "//",
   "Timing"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[26]:=",
 CellID->237838384],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{"0.028382`", ",", "0"}], "}"}], TraditionalForm]], "Output",
 ImageSize->{88, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[26]="]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"Clear", "[", "t", "]"}], ";"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[27]:=",
 CellID->1890146765],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"DeltaFunction", "[", 
     RowBox[{"1", "-", "x"}], "]"}], " ", 
    RowBox[{"f", "[", "x", "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[28]:=",
 CellID->593727658],

Cell[BoxData[
 FormBox[
  RowBox[{"f", "(", "1", ")"}], TraditionalForm]], "Output",
 ImageSize->{34, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[28]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    SuperscriptBox["x", "5"], 
    RowBox[{
     RowBox[{"Log", "[", 
      RowBox[{"1", "+", "x"}], "]"}], "^", "2"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[29]:=",
 CellID->1759046432],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"46", " ", 
     RowBox[{"log", "(", "2", ")"}]}], "45"], "-", 
   FractionBox["6959", "10800"]}], TraditionalForm]], "Output",
 ImageSize->{126, 35},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[29]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"N", "@", "%"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[30]:=",
 CellID->1795528063],

Cell[BoxData[
 FormBox["0.06419859938720329`", TraditionalForm]], "Output",
 ImageSize->{65, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[30]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"NIntegrate", "[", 
  RowBox[{
   RowBox[{
    SuperscriptBox["x", "5"], 
    RowBox[{
     RowBox[{"Log", "[", 
      RowBox[{"1", "+", "x"}], "]"}], "^", "2"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[31]:=",
 CellID->190638847],

Cell[BoxData[
 FormBox["0.06419859938720252`", TraditionalForm]], "Output",
 ImageSize->{65, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[31]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Integrate2", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"x", "^", 
     RowBox[{"(", 
      RowBox[{"OPEm", "-", "1"}], ")"}]}], 
    SuperscriptBox[
     RowBox[{"Log", "[", 
      RowBox[{"1", "+", "x"}], "]"}], "2"]}], ",", 
   RowBox[{"{", 
    RowBox[{"x", ",", "0", ",", "1"}], "}"}]}], "]"}]], "Input",
 CellTags->"Integrate2",
 CellLabel->"In[32]:=",
 CellID->1701338238],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", 
    FractionBox[
     RowBox[{"2", " ", 
      SuperscriptBox[
       RowBox[{"(", 
        RowBox[{"-", "1"}], ")"}], "m"], " ", 
      RowBox[{
       SubsuperscriptBox["S", "1", "2"], "(", 
       FormBox["m",
        TraditionalForm], ")"}]}], "m"]}], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox[
       FractionBox[
        RowBox[{"m", "-", "1"}], "2"],
       TraditionalForm], ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "-", 
   FractionBox[
    RowBox[{
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox[
       FractionBox[
        RowBox[{"m", "-", "1"}], "2"],
       TraditionalForm], ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox[
       FractionBox["m", "2"],
       TraditionalForm], ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox[
       FractionBox["m", "2"],
       TraditionalForm], ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{
      SubscriptBox["S", "2"], "(", 
      FormBox[
       FractionBox[
        RowBox[{"m", "-", "1"}], "2"],
       TraditionalForm], ")"}]}], 
    RowBox[{"2", " ", "m"}]], "-", 
   FractionBox[
    RowBox[{
     SubscriptBox["S", "2"], "(", 
     FormBox[
      FractionBox[
       RowBox[{"m", "-", "1"}], "2"],
      TraditionalForm], ")"}], 
    RowBox[{"2", " ", "m"}]], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{
      SubscriptBox["S", "2"], "(", 
      FormBox[
       FractionBox["m", "2"],
       TraditionalForm], ")"}]}], 
    RowBox[{"2", " ", "m"}]], "+", 
   FractionBox[
    RowBox[{
     SubscriptBox["S", "2"], "(", 
     FormBox[
      FractionBox["m", "2"],
      TraditionalForm], ")"}], 
    RowBox[{"2", " ", "m"}]], "-", 
   FractionBox[
    RowBox[{"2", " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{
      SubscriptBox["S", "2"], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "-", 
   FractionBox[
    RowBox[{"2", " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{
      SubscriptBox["S", 
       RowBox[{"-", "11"}]], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{"4", " ", 
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], "m"], " ", 
     RowBox[{"log", "(", "2", ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox["m",
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], 
      RowBox[{"m", "+", "1"}]], " ", 
     RowBox[{"log", "(", "2", ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox[
       FractionBox[
        RowBox[{"m", "-", "1"}], "2"],
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     RowBox[{"log", "(", "2", ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox[
       FractionBox[
        RowBox[{"m", "-", "1"}], "2"],
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], 
      RowBox[{"m", "+", "1"}]], " ", 
     RowBox[{"log", "(", "2", ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox[
       FractionBox["m", "2"],
       TraditionalForm], ")"}]}], "m"], "-", 
   FractionBox[
    RowBox[{
     RowBox[{"log", "(", "2", ")"}], " ", 
     RowBox[{
      SubscriptBox["S", "1"], "(", 
      FormBox[
       FractionBox["m", "2"],
       TraditionalForm], ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox[
      RowBox[{"(", 
       RowBox[{"-", "1"}], ")"}], 
      RowBox[{"m", "+", "1"}]], " ", 
     RowBox[{
      SuperscriptBox["log", "2"], "(", "2", ")"}]}], "m"], "+", 
   FractionBox[
    RowBox[{
     SuperscriptBox["log", "2"], "(", "2", ")"}], "m"]}], 
  TraditionalForm]], "Output",
 ImageSize->{514, 311},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"Integrate2",
 CellLabel->"Out[32]="]
}, Open  ]]
}, Open  ]],

Cell["", "SectionFooterSpacer"]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "See Also"
}], "SeeAlsoSection",
 WholeCellGroupOpener->True,
 CellID->1255426704],

Cell[TextData[{
 StyleBox[ButtonBox["DeltaFunction",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/DeltaFunction",
  ButtonNote->"DeltaFunction"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["Integrate3",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/Integrate3",
  ButtonNote->"Integrate3"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["Integrate4",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/Integrate4",
  ButtonNote->"Integrate4"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["Integrate5",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/Integrate5",
  ButtonNote->"Integrate5"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["SumS",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/SumS",
  ButtonNote->"SumS"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["SumT",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/SumT",
  ButtonNote->"SumT"],
  FontFamily->"Verdana"],
 "."
}], "SeeAlso"]
}, Open  ]],

Cell[" ", "FooterCell"]
},
Saveable->False,
ScreenStyleEnvironment->"Working",
WindowSize->{725, 750},
WindowMargins->{{-10, Automatic}, {Automatic, -8}},
WindowTitle->"Integrate2",
TaggingRules->{
 "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> 
  GridBox[{{
      RowBox[{
        ButtonBox[
        "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", 
         BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> 
    Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> 
  None, "RootCaptions" -> "", 
  "Metadata" -> {
   "built" -> "{2020, 6, 20, 19, 8, 3.276881}", 
    "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", 
    "keywords" -> {}, "specialkeywords" -> {}, 
    "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> 
    "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> 
    "None", "summary" -> 
    "Integrate2 is like Integrate, but : Integrate2[a_Plus, b__] := \
Map[Integrate2[#, b]&, a] ( more linear algebra and partial fraction \
decomposition is done) Integrate2[f[x] DeltaFunction[x], x] -> f[0] \
Integrate2[f[x] DeltaFunction[x0-x], x] -> f[x0]. Integrate2[f[x] \
DeltaFunction[a + b x], x] -> Integrate[f[x] (1/Abs[b]) DeltaFunction[a/b + \
x], x], where abs[b] -> b, if b is a Symbol, and if b = -c, then abs[-c] -> \
c, i.e., the variable contained in b is supposed to be positive. \\[Pi]^2 is \
replaced by 6 Zeta2. Integrate2[1/(1-y),{y,x,1}] is intepreted as \
distribution, i.e. as Integrate2[-1/(1-y)],{y, 0, x}] -> Log[1-y]. \
Integrate2[1/(1-x),{x,0,1}] -> 0.", "synonyms" -> {}, "tabletags" -> {}, 
    "title" -> "Integrate2", "titlemodifier" -> "", "windowtitle" -> 
    "Integrate2", "type" -> "Symbol", "uri" -> "FeynCalc/ref/Integrate2"}, 
  "SearchTextTranslated" -> ""},
CellContext->"Global`",
FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], 
   Cell[
    StyleData["Input"], CellContext -> "Global`"], 
   Cell[
    StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, 
  FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", 
  StyleDefinitions -> "Default.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "PrimaryExamplesSection"->{
  Cell[6744, 190, 387, 15, 31, "PrimaryExamplesSection",
   CellTags->"PrimaryExamplesSection",
   CellID->572860895]},
 "Integrate2"->{
  Cell[7376, 219, 443, 16, 27, "Input",
   CellTags->"Integrate2",
   CellID->524907050],
  Cell[7822, 237, 442, 16, 55, "Output",
   CellTags->"Integrate2"],
  Cell[8470, 265, 299, 10, 27, "Input",
   CellTags->"Integrate2",
   CellID->546710902],
  Cell[8772, 277, 316, 10, 37, "Output",
   CellTags->"Integrate2"],
  Cell[9125, 292, 293, 10, 27, "Input",
   CellTags->"Integrate2",
   CellID->89878903],
  Cell[9421, 304, 431, 15, 55, "Output",
   CellTags->"Integrate2"],
  Cell[9889, 324, 355, 12, 27, "Input",
   CellTags->"Integrate2",
   CellID->1742557754],
  Cell[10247, 338, 661, 23, 59, "Output",
   CellTags->"Integrate2"],
  Cell[10945, 366, 336, 11, 27, "Input",
   CellTags->"Integrate2",
   CellID->1356840886],
  Cell[11284, 379, 219, 7, 37, "Output",
   CellTags->"Integrate2"],
  Cell[13084, 444, 289, 10, 27, "Input",
   CellTags->"Integrate2",
   CellID->1084770727],
  Cell[13376, 456, 191, 6, 35, "Output",
   CellTags->"Integrate2"],
  Cell[14232, 492, 336, 11, 27, "Input",
   CellTags->"Integrate2",
   CellID->1725124689],
  Cell[14571, 505, 191, 6, 35, "Output",
   CellTags->"Integrate2"],
  Cell[14799, 516, 405, 14, 27, "Input",
   CellTags->"Integrate2",
   CellID->1940746510],
  Cell[15207, 532, 249, 8, 37, "Output",
   CellTags->"Integrate2"],
  Cell[15493, 545, 435, 15, 27, "Input",
   CellTags->"Integrate2",
   CellID->582396558],
  Cell[15931, 562, 264, 10, 55, "Output",
   CellTags->"Integrate2"],
  Cell[16232, 577, 347, 12, 27, "Input",
   CellTags->"Integrate2",
   CellID->845490247],
  Cell[16582, 591, 246, 9, 37, "Output",
   CellTags->"Integrate2"],
  Cell[16865, 605, 374, 13, 27, "Input",
   CellTags->"Integrate2",
   CellID->1121674397],
  Cell[17242, 620, 396, 14, 56, "Output",
   CellTags->"Integrate2"],
  Cell[17675, 639, 333, 11, 27, "Input",
   CellTags->"Integrate2",
   CellID->1584122311],
  Cell[18011, 652, 275, 9, 37, "Output",
   CellTags->"Integrate2"],
  Cell[18323, 666, 301, 10, 27, "Input",
   CellTags->"Integrate2",
   CellID->1907301251],
  Cell[18627, 678, 383, 14, 55, "Output",
   CellTags->"Integrate2"],
  Cell[19047, 697, 465, 16, 27, "Input",
   CellTags->"Integrate2",
   CellID->1237143526],
  Cell[19515, 715, 556, 19, 60, "Output",
   CellTags->"Integrate2"],
  Cell[20108, 739, 741, 25, 45, "Input",
   CellTags->"Integrate2",
   CellID->2080558124],
  Cell[20852, 766, 5608, 188, 372, "Output",
   CellTags->"Integrate2"],
  Cell[26497, 959, 490, 17, 27, "Input",
   CellTags->"Integrate2",
   CellID->204763000],
  Cell[26990, 978, 906, 32, 56, "Output",
   CellTags->"Integrate2"],
  Cell[27933, 1015, 587, 20, 70, "Input",
   CellTags->"Integrate2",
   CellID->1234589200],
  Cell[28523, 1037, 5325, 180, 206, "Output",
   CellTags->"Integrate2"],
  Cell[33885, 1222, 162, 5, 27, "Input",
   CellTags->"Integrate2",
   CellID->1839623139],
  Cell[34050, 1229, 1777, 56, 139, "Output",
   CellTags->"Integrate2"],
  Cell[35864, 1290, 124, 4, 27, "Input",
   CellTags->"Integrate2",
   CellID->1653791497],
  Cell[35991, 1296, 212, 6, 35, "Output",
   CellTags->"Integrate2"],
  Cell[36240, 1307, 704, 24, 78, "Input",
   CellTags->"Integrate2",
   CellID->1526670238],
  Cell[36947, 1333, 3820, 144, 194, "Output",
   CellTags->"Integrate2"],
  Cell[40804, 1482, 169, 5, 27, "Input",
   CellTags->"Integrate2",
   CellID->20428829],
  Cell[40976, 1489, 195, 6, 35, "Output",
   CellTags->"Integrate2"],
  Cell[41208, 1500, 387, 13, 27, "Input",
   CellTags->"Integrate2",
   CellID->512808203],
  Cell[41598, 1515, 192, 6, 35, "Output",
   CellTags->"Integrate2"],
  Cell[41943, 1531, 302, 9, 29, "Input",
   CellTags->"Integrate2",
   CellID->18981591],
  Cell[42248, 1542, 5465, 177, 394, "Output",
   CellTags->"Integrate2"],
  Cell[57842, 2051, 249, 9, 27, "Input",
   CellTags->"Integrate2",
   CellID->182134904],
  Cell[58094, 2062, 247, 8, 37, "Output",
   CellTags->"Integrate2"],
  Cell[58522, 2080, 345, 12, 27, "Input",
   CellTags->"Integrate2",
   CellID->237838384],
  Cell[58870, 2094, 247, 8, 37, "Output",
   CellTags->"Integrate2"],
  Cell[59132, 2105, 146, 5, 27, "Input",
   CellTags->"Integrate2",
   CellID->1890146765],
  Cell[59303, 2114, 336, 11, 27, "Input",
   CellTags->"Integrate2",
   CellID->593727658],
  Cell[59642, 2127, 220, 7, 37, "Output",
   CellTags->"Integrate2"],
  Cell[59899, 2139, 345, 12, 33, "Input",
   CellTags->"Integrate2",
   CellID->1759046432],
  Cell[60247, 2153, 327, 11, 56, "Output",
   CellTags->"Integrate2"],
  Cell[60611, 2169, 119, 4, 27, "Input",
   CellTags->"Integrate2",
   CellID->1795528063],
  Cell[60733, 2175, 211, 6, 35, "Output",
   CellTags->"Integrate2"],
  Cell[60981, 2186, 344, 12, 33, "Input",
   CellTags->"Integrate2",
   CellID->190638847],
  Cell[61328, 2200, 211, 6, 35, "Output",
   CellTags->"Integrate2"],
  Cell[61576, 2211, 401, 14, 33, "Input",
   CellTags->"Integrate2",
   CellID->1701338238],
  Cell[61980, 2227, 5031, 190, 332, "Output",
   CellTags->"Integrate2"]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"PrimaryExamplesSection", 70816, 2534},
 {"Integrate2", 70953, 2538}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[582, 21, 3479, 83, 53, "AnchorBarGrid",
 CellID->1],
Cell[4064, 106, 287, 11, 45, "ObjectNameGrid"],
Cell[CellGroupData[{
Cell[4376, 121, 1123, 24, 173, "Usage",
 CellID->982511436],
Cell[CellGroupData[{
Cell[5524, 149, 738, 24, 31, "NotesSection",
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->106623255],
Cell[6265, 175, 31, 0, 14, "SectionHeaderSpacer"],
Cell[6299, 177, 396, 7, 83, "Notes",
 CellID->1067943069]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[6744, 190, 387, 15, 31, "PrimaryExamplesSection",
 CellTags->"PrimaryExamplesSection",
 CellID->572860895],
Cell[CellGroupData[{
Cell[7156, 209, 195, 6, 26, "ExampleSection",
 CellID->439476420],
Cell[CellGroupData[{
Cell[7376, 219, 443, 16, 27, "Input",
 CellTags->"Integrate2",
 CellID->524907050],
Cell[7822, 237, 442, 16, 55, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[8279, 256, 166, 5, 32, "Notes"],
Cell[CellGroupData[{
Cell[8470, 265, 299, 10, 27, "Input",
 CellTags->"Integrate2",
 CellID->546710902],
Cell[8772, 277, 316, 10, 37, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9125, 292, 293, 10, 27, "Input",
 CellTags->"Integrate2",
 CellID->89878903],
Cell[9421, 304, 431, 15, 55, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9889, 324, 355, 12, 27, "Input",
 CellTags->"Integrate2",
 CellID->1742557754],
Cell[10247, 338, 661, 23, 59, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[10945, 366, 336, 11, 27, "Input",
 CellTags->"Integrate2",
 CellID->1356840886],
Cell[11284, 379, 219, 7, 37, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[11518, 389, 1541, 51, 86, "Notes"],
Cell[CellGroupData[{
Cell[13084, 444, 289, 10, 27, "Input",
 CellTags->"Integrate2",
 CellID->1084770727],
Cell[13376, 456, 191, 6, 35, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[13582, 465, 625, 23, 67, "Notes"],
Cell[CellGroupData[{
Cell[14232, 492, 336, 11, 27, "Input",
 CellTags->"Integrate2",
 CellID->1725124689],
Cell[14571, 505, 191, 6, 35, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[14799, 516, 405, 14, 27, "Input",
 CellTags->"Integrate2",
 CellID->1940746510],
Cell[15207, 532, 249, 8, 37, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[15493, 545, 435, 15, 27, "Input",
 CellTags->"Integrate2",
 CellID->582396558],
Cell[15931, 562, 264, 10, 55, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16232, 577, 347, 12, 27, "Input",
 CellTags->"Integrate2",
 CellID->845490247],
Cell[16582, 591, 246, 9, 37, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16865, 605, 374, 13, 27, "Input",
 CellTags->"Integrate2",
 CellID->1121674397],
Cell[17242, 620, 396, 14, 56, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[17675, 639, 333, 11, 27, "Input",
 CellTags->"Integrate2",
 CellID->1584122311],
Cell[18011, 652, 275, 9, 37, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[18323, 666, 301, 10, 27, "Input",
 CellTags->"Integrate2",
 CellID->1907301251],
Cell[18627, 678, 383, 14, 55, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[19047, 697, 465, 16, 27, "Input",
 CellTags->"Integrate2",
 CellID->1237143526],
Cell[19515, 715, 556, 19, 60, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[20108, 739, 741, 25, 45, "Input",
 CellTags->"Integrate2",
 CellID->2080558124],
Cell[20852, 766, 5608, 188, 372, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[26497, 959, 490, 17, 27, "Input",
 CellTags->"Integrate2",
 CellID->204763000],
Cell[26990, 978, 906, 32, 56, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[27933, 1015, 587, 20, 70, "Input",
 CellTags->"Integrate2",
 CellID->1234589200],
Cell[28523, 1037, 5325, 180, 206, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[33885, 1222, 162, 5, 27, "Input",
 CellTags->"Integrate2",
 CellID->1839623139],
Cell[34050, 1229, 1777, 56, 139, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[35864, 1290, 124, 4, 27, "Input",
 CellTags->"Integrate2",
 CellID->1653791497],
Cell[35991, 1296, 212, 6, 35, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[36240, 1307, 704, 24, 78, "Input",
 CellTags->"Integrate2",
 CellID->1526670238],
Cell[36947, 1333, 3820, 144, 194, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[40804, 1482, 169, 5, 27, "Input",
 CellTags->"Integrate2",
 CellID->20428829],
Cell[40976, 1489, 195, 6, 35, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[41208, 1500, 387, 13, 27, "Input",
 CellTags->"Integrate2",
 CellID->512808203],
Cell[41598, 1515, 192, 6, 35, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[41805, 1524, 113, 3, 32, "Notes"],
Cell[CellGroupData[{
Cell[41943, 1531, 302, 9, 29, "Input",
 CellTags->"Integrate2",
 CellID->18981591],
Cell[42248, 1542, 5465, 177, 394, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[47750, 1724, 79, 2, 27, "Input"],
Cell[47832, 1728, 9973, 318, 605, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[57842, 2051, 249, 9, 27, "Input",
 CellTags->"Integrate2",
 CellID->182134904],
Cell[58094, 2062, 247, 8, 37, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[58356, 2073, 141, 3, 49, "Notes"],
Cell[CellGroupData[{
Cell[58522, 2080, 345, 12, 27, "Input",
 CellTags->"Integrate2",
 CellID->237838384],
Cell[58870, 2094, 247, 8, 37, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[59132, 2105, 146, 5, 27, "Input",
 CellTags->"Integrate2",
 CellID->1890146765],
Cell[CellGroupData[{
Cell[59303, 2114, 336, 11, 27, "Input",
 CellTags->"Integrate2",
 CellID->593727658],
Cell[59642, 2127, 220, 7, 37, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[59899, 2139, 345, 12, 33, "Input",
 CellTags->"Integrate2",
 CellID->1759046432],
Cell[60247, 2153, 327, 11, 56, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[60611, 2169, 119, 4, 27, "Input",
 CellTags->"Integrate2",
 CellID->1795528063],
Cell[60733, 2175, 211, 6, 35, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[60981, 2186, 344, 12, 33, "Input",
 CellTags->"Integrate2",
 CellID->190638847],
Cell[61328, 2200, 211, 6, 35, "Output",
 CellTags->"Integrate2"]
}, Open  ]],
Cell[CellGroupData[{
Cell[61576, 2211, 401, 14, 33, "Input",
 CellTags->"Integrate2",
 CellID->1701338238],
Cell[61980, 2227, 5031, 190, 332, "Output",
 CellTags->"Integrate2"]
}, Open  ]]
}, Open  ]],
Cell[67038, 2421, 31, 0, 29, "SectionFooterSpacer"]
}, Open  ]],
Cell[CellGroupData[{
Cell[67106, 2426, 270, 12, 31, "SeeAlsoSection",
 CellID->1255426704],
Cell[67379, 2440, 991, 37, 56, "SeeAlso"]
}, Open  ]],
Cell[68385, 2480, 23, 0, 41, "FooterCell"]
}
]
*)

(* End of internal cache information *)

